Henri & Renaud Lifchitz's PRP Top records

What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!

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1-250	251-500	501-750	751-1000	1001-1250	1251-1500	1501-1750	1751-2000
2001-2250	2251-2500	2501-2750	2751-3000	3001-3250	3251-3500	3501-3750	3751-4000
4001-4250	4251-4500	4501-4750	4751-5000	5001-5250	5251-5500	5501-5750	5751-6000
6001-6250	6251-6500	6501-6750	6751-7000	7001-7250	7251-7500	7501-7750	7751-8000
8001-8250	8251-8500	8501-8750	8751-9000	9001-9250	9251-9500	9501-9750	9751-10000

Rank	Probable prime	Digits (> 50000)	Who ?	When ?
8001	2^218680-719	65830	Yves Minet	05/2012
8002	18^52424+17	65807	Lelio R Paula	08/2013
8003	19062^2827+2827^19062	65790	Hans Havermann	08/2019
8004	(2*15683^15683+1)/732384425	65789	David Broadhurst	09/2010
8005	(23*2^218517+1)/19003	65778	Lelio R Paula	07/2012
8006	(5*10^65773+1)/3	65774	Erik Branger	12/2013
8007	160^29839-159	65769	Norbert Schneider	12/2018
8008	2^218457-17329	65763	Enzo Doria	05/2013
8009	151703#+223381	65759	Nicolas PALAU	10/2016
8010	2^218436+40755	65756	Lelio R Paula	10/2011
8011	2^218399-4627	65745	Yves Minet	05/2019
8012	(F(44)^7433-F(43)^7433)/F(42)	65744	Wayne Halsdorf	03/2012
8013	15952^13219+13219^15952	65742	Hans Havermann	08/2019
8014	157^29934+29934^157	65733	Serge Batalov	05/2014
8015	211^28273-2	65715	Lelio R Paula	09/2013
8016	(59*10^65712+31)/9	65713	Robert Price	09/2015
8017	611^23586+23586^611	65712	Norbert Schneider	08/2016
8018	p(13991)#/2+32	65712	Robert Price	12/2016
8019	15865^13864+13864^15865	65712	Hans Havermann	07/2019
8020	2^218282-18485	65710	Enzo Doria	05/2013
8021	2^218274-111251	65708	Enzo Doria	05/2014
8022	2*F(314335)-1	65693	Henri Lifchitz	12/2009
8023	2^218200+427	65685	Henri Lifchitz	01/2005
8024	(10199^16384+10197^16384)/2	65676	Jeppe Stig Nielsen	04/2018
8025	(10199^(2^14)+(10197)^(2^14))/2	65676	Robert Price	05/2018
8026	46532!3+3	65667	Robert Price	10/2014
8027	2^218120-147	65661	Lelio R Paula	08/2011
8028	452^24729+24729^452	65659	Norbert Schneider	09/2016
8029	5817^17440+17440^5817	65657	Norbert Schneider	06/2019
8030	2^218102-114893	65656	Enzo Doria	05/2015
8031	(15*2^218083-1)/17	65650	Lelio R Paula	01/2014
8032	(15*2^218081+1)/18941	65646	Lelio R Paula	08/2012
8033	15818^14115+14115^15818	65640	Hans Havermann	08/2019
8034	(306^26407-1)/305	65638	Eric Chen	09/2017
8035	19^51326+36	65634	Lelio R Paula	08/2013
8036	(21*2^218045-1)/451583	65634	Lelio R Paula	01/2014
8037	2^217989-33	65622	Lelio R Paula	08/2011
8038	(13*2^217961+1)/3	65614	Lelio R Paula	06/2012
8039	4*6^84315-5	65611	Lelio R Paula	09/2014
8040	(315047^11933+1)/315048	65607	Faysal YAtim	06/2008
8041	6^84303+55	65601	Lelio R Paula	07/2013
8042	16585^9024+9024^16585	65601	Hans Havermann	08/2019
8043	18462^3575+3575^18462	65601	Hans Havermann	08/2019
8044	15963^12862+12862^15963	65597	Hans Havermann	08/2019
8045	(-lucasV(1,2,435857)+2)/(1738598017)	65595	Mike Oakes	04/2017
8046	(9787*2^217873-1)/37	65589	Lelio R Paula	04/2015
8047	5*2^217858+3	65583	Lelio R Paula	04/2014
8048	(19*10^65572+119)/3	65573	Robert Price	02/2017
8050	20^50399+51	65571	Lelio R Paula	08/2013
8049	7162^17009+17009^7162	65571	Norbert Schneider	07/2018
8051	11^62946-5670	65552	Enzo Doria	01/2013
8052	2^217742-3911	65547	Yves Minet	08/2009
8053	(19*10^65545+77)/3	65546	Robert Price	08/2016
8054	2^217731+131	65544	Lelio R Paula	08/2011
8055	2^217720-111287	65541	Enzo Doria	05/2014
8056	(365^25579+1)/366	65539	Eric Chen	10/2017
8057	10^65537+27	65538	Robert Price	01/2011
8058	10^65537-76859	65537	Patrick De Geest	05/2013
8059	(28*10^65532+359)/9	65533	Robert Price	11/2017
8060	(10223*2^217676+1)/3	65531	Lelio R Paula	06/2014
8061	PadovanNumber[536485]	65518	Eric W. Weisstein	05/2009
8062	5*10^65509+23	65510	Robert Price	11/2017
8063	(8*10^65507-83)/3	65508	Robert Price	10/2017
8064	7*10^65492-47	65493	Robert Price	02/2017
8065	2^217547-1868407	65489	Enzo Doria	04/2016
8066	2^217531-111769	65484	Enzo Doria	05/2014
8067	7^77484-18	65482	Lelio R Paula	06/2013
8068	5754^17413+17413^5754	65473	Norbert Schneider	05/2019
8069	2^217488-113285	65471	Enzo Doria	07/2014
8070	151153#/30-30	65468	Henri Lifchitz	12/2011
8071	2^217466+4257	65464	Lelio R Paula	10/2011
8072	46396!3-81	65455	Robert Price	09/2014
8073	2^217421-113185	65451	Enzo Doria	07/2014
8074	(6883*2^217440-1)/1061193295893	65448	Lelio R Paula	04/2015
8075	2^217408-2145	65447	Lelio R Paula	10/2011
8076	2^217398-16947	65444	Enzo Doria	05/2013
8077	16097^11628+11628^16097	65443	Hans Havermann	07/2019
8078	8*5^93613+3	65434	Lelio R Paula	09/2014
8079	15929^12810+12810^15929	65430	Hans Havermann	07/2019
8080	11^62828-5310	65429	Enzo Doria	01/2013
8081	10^65426+13	65427	Robert Price	01/2011
8082	2^217341-6555	65427	Lelio R Paula	10/2011
8083	10^65426-54849	65426	Patrick De Geest	05/2013
8084	(21*2^217363-1)/56003626667	65424	Lelio R Paula	01/2014
8085	30011^14608-108	65405	Enzo Doria	07/2012
8086	119^31504-2	65389	Lelio R Paula	10/2017
8087	(43^40031-1)/42	65388	Robert Price	04/2014
8088	2^217190+94395	65381	Henri Lifchitz	02/2005
8089	15^55587+46	65376	Lelio R Paula	08/2013
8090	18443^3502+3502^18443	65368	Hans Havermann	07/2019
8091	2^217088-111833	65350	Enzo Doria	05/2014
8092	(13*2^217069-1)/1682945	65340	Lelio R Paula	01/2014
8093	(10^65340+47)/3	65340	Robert Price	11/2017
8094	(62*10^65331+1)/9	65332	Serge Batalov	11/2010
8095	2^216947-111351	65308	Enzo Doria	05/2014
8096	-E(18022)/775201845682685322943949235068359	65307	Thomas Ritschel	02/2017
8097	(13*10^65297+83)/3	65298	Robert Price	09/2016
8098	16413^9502+9502^16413	65288	Hans Havermann	07/2019
8099	5^93400-8	65284	Lelio R Paula	06/2013
8100	2^216802-165	65264	Lelio R Paula	08/2011
8101	2^216799-28635	65264	Lelio R Paula	10/2011
8102	5*10^65255+51	65256	Robert Price	01/2017
8103	2^216762-167	65252	Lelio R Paula	08/2011
8104	11^62657-5790	65251	Enzo Doria	01/2013
8105	3^136756-112880	65250	Enzo Doria	06/2014
8106	2^216752+21	65249	Lelio R Paula	08/2011
8107	3*10^65247+11	65248	Robert Price	11/2017
8108	11^62651-2700	65245	Enzo Doria	12/2012
8109	15130^15609-15609^15130	65244	Norbert Schneider	07/2018
8110	Pell-LucasQ(170413)/2	65230	Eric W. Weisstein	12/2006
8111	gcd(V(790525),5F(158105)(F(158105)+1)+1)	65230	Serge Batalov	04/2015
8112	(2^216676-1017)/637	65224	Lelio R Paula	04/2012
8113	2^216652-2327	65219	Yves Minet	10/2013
8114	(9179*2^216648-1)/4667	65218	Lelio R Paula	04/2015
8115	(5*10^65203-119)/3	65204	Robert Price	04/2016
8116	15977^12034+12034^15977	65193	Hans Havermann	07/2019
8117	2^216555-113269	65190	Enzo Doria	07/2014
8119	(9513^16384+1)/2	65181	Henri Lifchitz	02/2007
8118	15753^13730+13730^15753	65181	Hans Havermann	07/2019
8120	2^216474+12915	65166	Lelio R Paula	02/2013
8121	19^50958-32	65163	Lelio R Paula	08/2013
8122	2^216442-112133	65156	Enzo Doria	06/2014
8123	2^216437-112213	65155	Enzo Doria	06/2014
8124	2^216435-112767	65154	Enzo Doria	06/2014
8125	2^216420+12705	65149	Lelio R Paula	02/2013
8126	8*3^136507-7	65132	Lelio R Paula	04/2014
8127	(-lucasV(1,2,432719)-2)/(5*461)	65128	Mike Oakes	03/2017
8128	16803^7496+7496^16803	65109	Hans Havermann	07/2019
8129	15132^15575-15575^15132	65102	Norbert Schneider	07/2018
8130	5*10^65086-51	65087	Robert Price	10/2017
8131	2^216197-111769	65082	Enzo Doria	05/2014
8132	6^83631-79	65078	Lelio R Paula	07/2013
8133	572^23601+23601^572	65078	Norbert Schneider	08/2016
8135	(3^136399-7)/544220	65074	Lelio R Paula	04/2012
8134	15592^14911+14911^15592	65074	Hans Havermann	07/2019
8136	2^216154-1421	65069	Yves Minet	01/2013
8137	2^216145-112663	65067	Enzo Doria	06/2014
8138	(7*10^65064+53)/3	65065	Robert Price	10/2017
8139	132013*10^65050+2^216091-1	65056	Gilbert Mozzo	01/2014
8140	132019*10^65050+2^216091-1	65056	Gilbert Mozzo	01/2014
8141	148918*10^65050+2^216091-1	65056	Gilbert Mozzo	02/2014
8142	194014*10^65050+2^216091-1	65056	Gilbert Mozzo	02/2014
8143	223864*10^65050+2^216091-1	65056	Gilbert Mozzo	04/2014
8146	82090*10^65050+2^216091-1	65055	Gilbert Mozzo	07/2012
8145	95133*10^65050+2^216091-1	65055	Gilbert Mozzo	12/2013
8144	98142*10^65050+2^216091-1	65055	Gilbert Mozzo	12/2013
8147	((2^216091-1)*34009-48)/25	65054	Serge Batalov	01/2012
8148	5977*10^65050+2^216091-1	65054	Gilbert Mozzo	03/2012
8149	7*2^216091+2^298-13	65051	Peter Lesala	03/2007
8150	2^216091+2*29208-1	65050	Makoto Morimoto	10/2013
8151	15845^12736+12736^15845	65045	Hans Havermann	07/2019
8152	(10^(232521+1)-610^32521-1)/3	65043	Robert Price	02/2016
8153	p(13861)#/2+256	65039	Robert Price	05/2017
8154	(2^216091-2096)/(2^432918437*5220283)	65036	Makoto Morimoto	10/2017
8155	11^62439-4380	65024	Enzo Doria	01/2013
8156	16489^8776+8776^16489	65022	Hans Havermann	07/2019
8157	3^136244+2	65005	Mike Oakes	11/2009
8158	13^58343-50	64991	Lelio R Paula	07/2013
8159	331^25791-10002	64989	Enzo Doria	07/2012
8160	2^215877+131	64986	Lelio R Paula	08/2011
8161	4*5^92959+9	64977	Lelio R Paula	09/2014
8162	2^215789-18825	64959	Lelio R Paula	09/2011
8163	(2^215801-509203)/41327	64958	Lelio R Paula	05/2012
8164	U(315311)	64954	Serge Batalov	03/2015
8165	46072!3-59049	64951	Robert Price	12/2015
8166	2^215750-5955	64948	Lelio R Paula	09/2011
8167	13^58281+46	64922	Lelio R Paula	07/2013
8168	15633^14212+14212^15633	64919	Hans Havermann	07/2019
8169	2^215623+183	64909	Lelio R Paula	08/2011
8170	(46*10^64904+521)/9	64905	Robert Price	08/2017
8171	(3^136043-2^136043)/(19862279*33466579)	64895	Mike Oakes	12/2016
8172	5*2^215554+3	64889	Lelio R Paula	04/2014
8173	2^215541-112075	64885	Enzo Doria	06/2014
8174	2*10^64882-3	64883	Dmitry Domanov	11/2010
8175	16592^8121+8121^16592	64869	Hans Havermann	07/2019
8176	10^64862+342339	64863	Patrick De Geest	05/2013
8177	10^64862-47	64862	Robert Price	05/2011
8178	19^50718-84	64856	Lelio R Paula	08/2013
8179	(30452^215471-1)/(17115127067173473)	64853	Jens K. Andersen	09/2007
8180	86413!6-12	64846	Robert Price	08/2018
8181	10^64843+4278697839	64844	Robert Price	05/2015
8182	10^64843+21967	64844	Patrick De Geest	03/2016
8183	10^64843-340073	64843	Patrick De Geest	03/2016
8184	11^62254+70	64831	Lelio R Paula	07/2013
8185	2^215351-111925	64828	Enzo Doria	05/2014
8186	2^215310-117	64815	Lelio R Paula	08/2011
8187	124^30958-123	64809	Norbert Schneider	02/2015
8188	(7*10^64807+17)/3	64808	Erik Branger	03/2014
8189	(710^(232400+1)-27*10^32400-7)/9	64801	Robert Price	11/2015
8190	2^215243-15949	64795	Enzo Doria	04/2013
8191	23^47581-22^47581	64793	Robert Price	08/2012
8192	(62*10^64783-17)/9	64784	Robert Price	09/2015
8193	5*3^135747-4	64769	Lelio R Paula	04/2014
8194	(59*10^64767-41)/9	64768	Robert Price	09/2015
8196	(2^215140+3)/19	64763	Lelio R Paula	04/2012
8195	2^215135-17169	64763	Enzo Doria	05/2013
8197	16078^10665+10665^16078	64762	Hans Havermann	07/2019
8198	2^215115-111277	64757	Enzo Doria	05/2014
8199	9*5^92641+2	64755	Lelio R Paula	09/2014
8200	(lucasV(1,2,430086)-2)/(7*1033)	64731	Mike Oakes	03/2017
8201	5791^17200+17200^5791	64720	Norbert Schneider	12/2018
8202	(5*10^64715-23)/9	64715	Robert Price	11/2014
8203	2^214938-1781	64703	Yves Minet	03/2013
8204	21003^1202+1202^21003	64688	Hans Havermann	07/2019
8205	11^62111-420	64682	Enzo Doria	08/2012
8206	18870^2677+2677^18870	64680	Hans Havermann	07/2019
8207	5^92525+42	64673	Lelio R Paula	06/2013
8208	2^214824+71893	64669	Enzo Doria	04/2016
8209	19157^2374+2374^19157	64665	Hans Havermann	08/2019
8210	2^214799-2221	64661	Yves Minet	08/2013
8211	18393^3274+3274^18393	64653	Hans Havermann	07/2019
8212	5939^17128+17128^5939	64637	Norbert Schneider	10/2018
8213	(21*2^214688+1)/293	64627	Lelio R Paula	08/2012
8214	92^32907+32907^92	64623	Serge Batalov	05/2014
8215	17650^4579+4579^17650	64613	Hans Havermann	07/2019
8216	(89*10^64608-539)/9	64609	Robert Price	11/2017
8217	6^83013+101	64597	Lelio R Paula	07/2013
8218	p(13775)#/2+8	64594	Robert Price	01/2017
8219	(7*10^64568-43)/9	64568	Robert Price	10/2014
8220	Pell-LucasQ(168677)/2	64566	Eric W. Weisstein	11/2006
8221	(24737*2^214476+1)/2877	64565	Lelio R Paula	06/2014
8222	(47*2^214463+1)/7	64561	Lelio R Paula	04/2015
8223	2^214458+54615	64559	Lelio R Paula	10/2011
8224	(3^135322+7)/122911408	64557	Lelio R Paula	04/2012
8225	2^214389-683113	64538	Paul Bourdelais	03/2013
8226	(76*10^64534+113)/9	64535	Robert Price	11/2017
8227	2^214369-111241	64532	Enzo Doria	05/2014
8228	(19^50461+3^50461)/22	64526	Robert Price	07/2013
8229	11^61954-3660	64519	Enzo Doria	12/2012
8230	(23*2^214319-1)/21	64517	Lelio R Paula	01/2014
8231	(58695*2^214310-1)/571	64516	Lelio R Paula	04/2015
8232	2^214300-4547	64511	Yves Minet	03/2019
8233	35^41779-34	64510	Norbert Schneider	04/2014
8234	(159^29303+1)/160	64506	Eric Chen	12/2017
8235	(89*10^64504-179)/9	64505	Robert Price	11/2017
8236	11^61939-5220	64503	Enzo Doria	01/2013
8237	(2^214271+78557)/35	64501	Lelio R Paula	05/2012
8238	L(308604)+P(308604)	64495	Robert Price	12/2017
8239	126^30706-125	64494	Norbert Schneider	02/2015
8240	gcd(V(1157265),5F(231453)(F(231453)-1)+1)	64492	Serge Batalov	04/2015
8241	2^214215+12909	64486	Lelio R Paula	10/2011
8242	16581^7738+7738^16581	64478	Hans Havermann	07/2019
8243	5^92225+66	64463	Lelio R Paula	06/2013
8244	2^214126-240551	64459	Paul Bourdelais	03/2013
8245	8*6^82827+5	64453	Lelio R Paula	09/2014
8246	(31*2^214120-1)/2170485	64452	Lelio R Paula	01/2014
8247	(31*2^214088-1)/5955	64445	Lelio R Paula	01/2014
8248	14^56227+89	64444	Lelio R Paula	08/2013
8249	10^64436+2667	64437	Patrick De Geest	05/2013
8250	65^35543-64^35543	64437	Robert Price	08/2013

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Probable Primes Top 10000

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